Nonquasineutral current equilibria as elementary structures of plasma dynamics

A study is made of the fundamental features of current filaments with a nonzero electron vorticity Ω _e ≡ B − (c/e) ▿ × p _ee ≠ 0 and the corresponding Lagrangian invariant I _e . Such current structures can exist on spatial scales of up to ω _pi ⁻¹. It is shown that the dissipative stage of the plasma evolution and the violation of Thomson’s theorem on vorticity conservation in an electron fluid are of fundamental importance for the onset of electron current structures. A key role of the screening of electric and magnetic fields at distances on the order of the magnetic Debye radius r _B = B/(4πen _e )—the main property of such current structures in a Hall medium with σB/(en _e c) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c/ω _pe , the structures under consideration correspond to the condition r _B > c/ω _pe or B ² > 4πn _e m _e c ², which leads to strong charge separation in the filament and relativistic electron drift. It is demonstrated that the specific energy content in current structures is high at a filament current of 10–15 kA: from 100 J/cm³ at a plasma density of 10¹⁴ cm⁻³ (the parameters of a lightning leader) to 10⁷ J/cm³ for a fully ionized atmospheric-pressure air. Estimates are presented showing that the Earth’s ionosphere, circumsolar space, and interstellar space are all Hall media in which current vortex structures can occur. A localized cylindrical equilibrium with a magnetic field reversal is constructed—an equilibrium that correlates with the magnetic structures observed in intergalactic space. It is shown that a magnetized plasma can be studied by using evolutionary equations for the electron and ion Lagrangian invariants I _e and I _i . An investigation is carried out of the evolution of a current-carrying plasma in a cylinder with a strong external magnetic field and with a longitudinal electron current turned on in the initial stage—an object that can serve as the simplest electrodynamic model of a tokamak. In this case, it is assumed that the plasma conductivity is low in the initial stage and then increases substantially with time. Based on the conservation of the integral momentum of the charged particles and electromagnetic field in a plasma cylinder within a perfectly conducting wall impenetrable by particles, arguments are presented in support of the generation of a radial electric field in a plasma cylinder and the production of drift ion fluxes along the cylinder axis. A hypothesis is proposed that the ionized intergalactic gas expands under the action of electromagnetic forces.     

Effective Size of Subpopulations in Early-Run Sockeye Salmon Oncorhynchus nerkafrom Azabach'e Lake (Kamchatka): The Effect of Density on Variance of Reproductive Success

Using Parensky's approach for estimating the number of breeding pairs, we determined effective subpopulation size N _e in early-run sockeye salmon Oncorhynchus nerka from Azabach'e Lake (Kamchatka) in 1977 through 1981. On average (over years and populations), biased sex ratio decreased N _e by 7% as compared to the number of fish on the spawning sites (N _i). High density reduced the N _e/N _i ratio by 62–66% because some fish were excluded from spawning. Dominance polygyny as compared to monogamy and random union of gametes could reduce N _e by about 17%.     

Diagnostics of a nonequilibrium nitrogen plasma from the emission spectra of the second positive system of N2

A method is proposed for determining the electron density N _e and the electric field E in the non-equilibrium nitrogen plasma of a low-pressure discharge from the spectra of the second positive system of N₂. The method is based on measuring the specific energy deposition in the plasma and the distribution of nitrogen molecules over the vibrational levels of the C ³Π _u state, as well as on modeling this distribution for a given energy deposition. The fitting parameters of the model are the values of N _e and E. A kinetic model of the processes governing the steady-state density of the C ³Π _u nitrogen molecules is developed. The testing of this method showed it to be quite reliable. The method is of particular interest for diagnosing electrodeless discharges and provides detailed information on the processes occurring in the discharge plasma. Preliminary data are obtained on the plasma parameters in a cavity microwave discharge and an electrode microwave discharge. In particular, it is found that the electric field in an electrode microwave discharge in nitrogen is lower than that in a hydrogen discharge. This effect is shown to be produced by stepwise and associative processes with the participation of excited particles in nitrogen.     

Reversible Electropermeabilization of Mammalian Cells by High-Intensity, Ultra-Short Pulses of Submicrosecond Duration

Mouse myeloma cells were electropermeabilized by single square-wave electric pulses with amplitudes of up to ∼150 kV/cm and durations of 10–100 nsec. The effects of the field intensity, pulse duration and medium conductivity on cell viability and field-induced uptake of molecules were analyzed by quantitative flow cytometry using the membrane-impermeable fluorescent dye propidium iodide as indicator molecule. Despite the extremely large field strengths, the majority of cells survived the exposure to ultra-short field pulses. The electrically induced dye uptake increased markedly with decreasing conductivity of the suspending medium. We assigned this phenomenon to the transient electrodeformation (stretching) force that assumes its maximum value if cells are suspended in low-conductivity media, i.e., if the external conductivity σ_e is smaller than that of the cytosol σ_i. The stretching force vanishes when σ_e is equal to or larger than σ_i. Due to their capability of delivering extremely large electric fields, the pulse power systems used here appear to be a promising tool for the electropermeabilization of very small cells and vesicles (including intracellular organelles, liposomes, etc.). Received: 15 May 2001/Revised: 20 July 2001     

Ambipolarity condition and possibility of multivalued steady-state solutions to transport equations in stellarators

The possibility of steady-state multivalued solutions to transport equations in stellarators is considered. It is shown that the ambipolarity condition is necessary but not sufficient to find the ambipolar electric field, because the functions entering into it (the plasma density and temperature, as well as their spatial derivatives) depend on the ambipolar field. To do this correctly, it is necessary to solve the full set of time-independent transport equations (including diffusion and heat conduction equations). The possible existence of multivalued solutions to this set of equations is analyzed numerically. It is shown that, under certain conditions that depend on the form and magnitude of particle and heat sources, such solutions can exist. Their form is determined by the initial value of the ambipolar field, the source magnitudes, and the boundary conditions. Discontinuous solutions in which the radial profile of the ambipolar field undergoes jumps are found. In this case, however, the particle and energy fluxes remain continuous, because the discontinuities of the electric field are balanced by the discontinuities of the density and temperature gradients.     

Formation of a Z-pinch during electromagnetic compression of a nonquasineutral current filament

A study is made of the structure of a relativistic current filament with the azimuthal magnetic field B_θ in the range 4πn _e m _e c²?B _θ ² 4πn _i m _i c², when the plasma quasineutrality near the filament axis is violated and a narrow peak in electron density is formed there. The ion dynamics in a strong radial electric field of the filament on time scales of about several inverse ion plasma frequencies ω _pi ^?1 is investigated. The initial ion pressure prevents the ion plasma component from compression to infinitely high densities under the action of the electric field and leads to the formation of a dense hot plasma core near the axis of the Z-pinch on time scales of about a dozen ω _pi ^?1 . The compression of the ion component in the axial region gives rise to a collisionless “unloading” shock wave that propagates away from the axis and is accompanied by the vanishing of the radial ion velocity behind the shock front, the accumulation of positive charge near the axis, and the formation of a steady-state ion density profile. It is shown theoretically that ion-ion dissipation manifests itself as the destruction of the hot core of the formed Z-pinch on picosecond time scales. This may serve to explain the explosions of “hot points” in a current-carrying plasma.     

First results from plasma density measurements in the FTU tokamak by means of a two-frequency pulsed time-of-flight refractometer

A pulsed time-of-flight refractometer was developed and tested to determine the mean plasma density in the T-11M tokamak by measuring the propagation time of nanosecond microwave pulses in plasma. Later, it was also proposed to use such an instrument to measure and control the mean plasma density in the ITER tokamak by probing the plasma with an extraordinary wave, the electric field of which is perpendicular to the magnetic field in plasma, in the transparency window at frequencies of 50–100 GHz. To avoid the effect of the density profile shape on the measurement results in the nonlinear mode of refractometer operation (near the cutoff), a system operating at two different probing frequencies was developed and tested. Such a system provides two values of the time delay, which can be used to estimate the peaking factor of the density distribution α and correctly determine the linear density 〈Nl〉, regardless of the density profile (assuming a smooth density profile of the form of N(ρ) = N(0)(1 − ρ²)^α, where N(0) is the central plasma density and ρ = r/a is the normalized plasma radius). The first experiments on density measurements in the FTU tokamak performed with this refractometer are described, and results from these experiments are presented. The formation of a thin dense plasma layer in the zone of a strong magnetic field (the so-called MARFE layer) at a relatively low (for FTU) plasma density of ∼6 × 10¹⁹ m⁻³ was detected. The thickness of this layer, determined from the refractometry data, agrees well with the data obtained using a digital camera.     

Critical responses of photosynthetic efficiency of goldspur apple tree to soil water variation in semiarid loess hilly area

Goldspur apple (Malus pumila cv. Goldspur) is one of the main fruit trees planted in semiarid loess hilly areas. The photosynthetic efficiency in leaves of eight-year-old trees were studied under different soil water conditions with a Li-6400 portable photosynthesis system and a Li-Cor1600 portable steady state porometer in order to explore the effects of soil water stress on photosynthesis and the suitable soil water content (SWC) for water-saving irrigation of apple orchards. The results showed that the leaf net photosynthetic rate (P _N), transpiration rate (E), water-use efficiency (WUE), stomatal conductance (g _s), intercellular CO₂ concentration (C _i), and stomatal limiting value (L _s) displayed different threshold responses to soil water variation. When SWC was within a range of about 60%–86% of field capacity (FC), P _N and E were maintained in a relative steady state. At an elevated level but below 60% of FC, both P _N and E decreased evidently with decreasing soil moisture. The SWC needed to support WUE in a relatively steady state and at a high level was in the range of about 50%–71% of FC. When SWC was less than 48% of FC, g _s and L _s declined with decreasing soil moisture, while C _i increased rapidly. Based on the analysis of the stomatal limitation of photosynthesis using two criteria (C _i and L _s) suggested by Farquhar and Sharkey, it was implied that the predominant cause of restricting P _N had changed from stomatal limitation to nonstomatal one under severe water stress. In terms of water-saving irrigation for enhancing water-use efficiency, it was concluded that in semiarid loess hilly areas, the suitable range of SWC for water-saving irrigation in goldspur apple orchards is in the range of about 50%–71% of FC, and the most severe degree of soil water stress tolerated for photosynthesis is about 48% of FC.     

Abundance and arrangement of single,double and bifurcated hydrogen bonds in protein α-helices: Statistical analysis of PDB-select

Statistics are collected and analyzed for the possibility of hydrogen bonding in the secondary structures of globular proteins, based on geometric criteria. Double and bifurcated bonds are considered as pairs of admissible H-bonds with two proton donors or two proton acceptors, respectively. Most of such bonds belong to peptide groups in α-helices, with O _i …N _{i + 3} nearly as frequent as O _i …N _{i + 4}; in contrast, most of the 3/10-helical segments are too short to have any. Alternating double and bifurcated bonds in α-helices form an apparently cooperative network structure. A typical α-helical segment perhaps carries two stretches of the H-bond network broken in the middle. The constituent H-bonds are nonlinear: the hydrogen atom is off the straight line connecting the proton donor and proton acceptor atoms. This deflection is larger for H _{i + 3} vs. bond line O _i −N _{i + 3} than for H _{i + 4} vs. O _i −N _{i + 4}, and though the two kinds of bond have about the same length (exceeding those typical of low-molecular compounds), O _i …N _{i + 4} must be stronger than O _i …N _{i + 3}. Double/bifurcated bonds are also not coplanar, i.e., hydrogen atoms are beyond the N…O…N (or O…N…O) plane. The text was submitted by the authors in English.     

Na+/H+ exchange in crayfish neurons: dependence on extracellular sodium and pH

Summary Intracellular pH (pH_i) regulation was studied in crayfish neurons with pH-, and Na⁺-sensitive microelectrodes. It was confirmed to involve both a HCO ₃ ^– -dependent and a HCO ₃ ^– -independent mechanism. The latter was identified as the amiloride-sensitive Na⁺/H⁺ exchange described in vertebrate cells. Its dependence on extracellular pH (pH_e) and Na⁺ concentration ([Na⁺]_e) was studied in CO₂-free external solutions at 20°C. The steady state pH_i and the rate constant (k) of the exponential pH_i recovery following an acid load were determined. At pH_e=7.5 and [Na⁺]_e=200 mM, the average steady state pH_i was 7.09±0.12 (as compared to 7.30±0.10 in the presence of 5 mM bicarbonate). The dependence of the rate constant of recovery on [Na⁺]_e could be described by Michaelis-Menten kinetics; at pH_e=7.5 the apparentK _m andK _max were 39 mM and 1.4 mmol·l^–1·min^–1, respectively. Decreasing pH_e reduced the rate of recovery, the variations ofk with pH_e conforming to a simple titration curve with an apparent pK of 7.05±0.21. These kinetic properties of the Na⁺/H⁺ exchange in crayfish neurons are similar to those described in vertebrate cells.Preliminary results were presented at the First International Congress of Comparative Physiology and Biochemistry (Liège, Belgium, 1984)     

On the analogy of stability of tangential discontinuities in hydrodynamics and in nonisothermal collisionless plasma

Analogy between stability of tangential discontinuities in an ideal liquid in conventional hydrodynamics and in collisionless nonisothermal plasma with T _e ≫ T _i is shown. The difference is due to specific features of dispersion of ion sound waves in nonisothermal plasma in the short-wavelength range, in which the lasma quasineutrality is violated and the dispersion curve tends to the ion Langmuir frequency.     

Study of the parameters of hydrogen-titanium plasma in a pulsed reflective discharge

The parameters of a dense (10¹³–10¹⁴ cm⁻³) plasma produced by ionization of a H₂ + Ti mixture in a moderate-power (W ≤ 10 MW) pulsed reflective discharge are investigated. The dynamics of the plasma density, the elemental composition of the generated plasma, the radial distribution of the electron density, the rotation velocity and frequency of the plasma layer with n _p ≥ n _cr, the radial electric field, the coefficient of plasma particle separation, and the coefficient of plasma recombination in the stage of plasma decay are determined.     

Turbulent dynamics of helical perturbations in the edge plasma of the T-10 tokamak

Turbulent dynamics of the edge plasma in the T-10 tokamak is simulated numerically by solving nonlinear MHD equations in the framework of the four-field {?, n, p _e , p _i } reduced two-fluid Braginskii hydro-dynamics. It is shown that the transition from ohmic to electron-cyclotron heating is accompanied by a decrease in the amplitudes of turbulent fluctuations in plasma. This is caused by the enhancement of longitudinal dissipation due to the increase in the electron temperature. However, phase relations between potential fluctuations of different modes change in such a way that the Reynolds turbulent force increases, which leads to an increase in the poloidal velocity in the direction of ion diamagnetic drift. Since the poloidal and ion diamagnetic drift velocities enter into the equation of the radial force balance for ions with different signs, the radial electric field decreases. The simulation results agree qualitatively with the results of experiments in the T-10 tokamak. The dependence of the radial electric field on the plasma density, ion pressure, and neutral density is also calculated.     

Impact of magnetic field inhomogeneity on electron cyclotron radiative loss in tokamak reactors

The potential importance of electron cyclotron (EC) emission in the local electron power balance in the steady-state regimes of ITER operation with high temperatures, as well as in the DEMO reactor, requires accurate calculation of the one-dimensional (over magnetic surfaces) distribution of the net radiated power density, P _EC(ρ). When the central electron temperature increases to ∼30 keV, the local EC radiative loss comprises a substantial fraction of the heating power from fusion alphas and is close to the total auxiliary NBI heating power, P _EC(0) ≃ 0.3P _α(0) ≃ P _aux(0). In the present paper, the model of EC radiative transport in an axisymmetric toroidal plasma is extended to the case of an inhomogeneous magnetic field B(R, Z). The impact of such inhomogeneity on local and total power losses is analyzed in the framework of this model by using the CYNEQ code. It is shown that, for the magnetic field B, temperature T _e , density n _e , and wall reflection coefficient R _w expected in ITER and DEMO, accurate simulations of the EC radiative loss require self-consistent 1.5D transport analysis (i.e., one-dimensional simulations of plasma transport and two-dimensional simulations of plasma equilibrium). It is shown that EC radiative transport can be described with good accuracy in the 1D approximation with the surface-averaged magnetic field, B(ρ) = 〈B(R, Z)〉 _ms . This makes it possible to substantially reduce the computational time required for time-dependent self-consistent 1.5D transport analysis. Benchmarking of the CYNEQ results with available results of the RAYTEC, EXACTEC, and CYTRAN codes is performed for various approximations of the magnetic field.     

Breeding without breeding: minimum fingerprinting effort with respect to the effective population size

We present a probabilistic model to minimize the fingerprinting effort associated with the implementation of the “breeding without breeding” scheme under partial pedigree reconstruction. Our approach is directed at achieving a declared target population’s minimum effective population size (N _e ), following the pedigree reconstruction and genotypic selection and is based on the graph theory algorithm. The primary advantage of the proposed method is to reduce the cost associated with fingerprinting before the implementation of the pedigree reconstruction for seed parent–offspring derived from breeding arboreta and production or natural populations. Stochastic simulation was conducted to test the method’s efficiency assuming a simple polygenic model and a single trait. Hypothetical population consisted of 30 parental trees that were paired at random (selfing excluded), resulting in 600 individuals (potential candidates for forwards selection). The male parentage was assumed initially unknown. The model was used to estimate the minimum genotyping sample size needed to reaching the prescribed N _e . Results were compared with the known pedigree data. The model was successful in revealing the true relationship pattern over the whole range of N _e . Two to three offspring entered genotyping to meet the N _e  = 2 while 41 to 43 were required to satisfy the N _e  = 14. Importantly, genetic gain was affected at the lower limits of the genotyping effort. Doubling the number of parents resulted in considerable reduction of the genotyping effort at higher N _e values.     

Interaction of maturation delay and nonlinear birth in population and epidemic models

 A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e⁻ d ₁ T−dN(t) governs the adult population, with the death rate in previous life stages d ₁≧0. Standard assumptions are made on B(N) so that a unique equilibrium N _e exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d ₁>0, as T increases the equilibrium N _e can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease that does not cause death is introduced into the population, a threshold parameter R ₀ is identified. When R ₀<1, the disease dies out; when R ₀>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations indicate that oscillations can also be induced by disease related death in a model with maturation delay. Received: 2 November 1998 / Revised version: 26 February 1999     

Steady-state vortex structure in a plasma with a strong magnetic field

A study is made of nonquasineutral vortex structures in a plasma with a magnetic field B _z in which the charges separate on a spatial scale equal to the magnetic Debye radius r _B=B _z/4πen _e. The electric field arising due to charge separation leads to radial expansion of the ions, thereby destroying the initial electron vortex. It is shown that the ion pressure gradient stops ion expansion in a nonquasineutral electron vortex and gives rise to a steady structure with a characteristic scale on the order of r _B. With the electron inertia taken into account in the hydrodynamic approximation, the magnetic vortex structure in a hot plas mamanifests itself in the appearance of a “hole” in the plasma density.     

Effective size of an Atlantic salmon (Salmo salar L.) metapopulation in Northern Spain

The genetic diversity of metapopulations is influenced not only by the effective sizes (N _e ) of individual subpopulations, but also by the total effective size of the metapopulation (meta-N _e ). We estimated meta-N _e of four neighbouring Atlantic salmon populations connected by gene flow using genetic estimates of subpopulation N _e s and migration rates derived from capture–recapture data. The meta-[^(N)]_e meta{\hbox{-}}\hat{N}_{e} was lower than the sum of [^(N)]_e \hat{N}_{e} s of the subpopulations, suggesting that genetic diversity harboured by the four river salmon metapopulation is lower than what would have been expected by viewing individual subpopulations separately. In addition, meta-[^(N)]_e meta{\hbox{-}}\hat{N}_{e} was found to be sensitive to changes in [^(N)]_e \hat{N}_{e} of the subpopulation from which net emigration rate was largest, so as that the genetic diversity of the metapopulation would be best preserved by avoiding any reductions in N _e of this subpopulation. Yet, this subpopulation is the one that has historically—and still is—experiencing the highest exploitation rate in the metapopulation system.     

Small effective population sizes of two remnant ocelot populations (<Emphasis Type="Italic">Leopardus pardalis albescens</Emphasis>) in the United States

Threatened populations are vulnerable to the effects of genetic drift and inbreeding, particularly when gene flow is low and the effective population size is small. Estimates of effective population size (N _e ) provide important information on the status of endangered populations that have experienced severe fragmentation and serve as indicators of genetic viability. Genetic data from microsatellite loci were used to estimate N _e for the 2 remaining populations of the endangered ocelot (Leopardus pardalis albescens) occurring in the United States. Several methods were used to calculate N _e , resulting in estimates ranging from N _e  = 8.0 (95% CI: 3.2–23.1) to 13.9 (95% CI: 7.7–25.1) for the population located at the Laguna Atascosa Wildlife Refuge in Cameron County, Texas. The ocelot population in Willacy County, Texas, had N _e estimates of 2.9 (95% CI: 1.7–5.6) and 3.1 (95% CI: 1.9–13.5), respectively. Estimates of N _e in both populations were below the critical value recommended for short-term viability.